Horizon: A Trajectory Optimization Framework for Robotic Systems

This paper presents Horizon, an open-source framework for trajectory optimization tailored to robotic systems that implements a set of tools to simplify the process of dynamic motion generation. Its user-friendly Python-based API allows designing the most complex robot motions using a simple and intuitive syntax. At the same time, the modular structure of Horizon allows for easy customization on many levels, providing several recipes to handle fixed and floating-base systems, contact switching, variable time nodes, multiple transcriptions, integrators and solvers to guarantee flexibility towards diverse tasks. The proposed framework relies on direct simultaneous methods to transcribe the optimal problem into a nonlinear programming problem that can be solved by state-of-the-art solvers. In particular, it provides several off-the-shelf solvers, as well as two custom-implemented solvers, i.e. GN-SQP and Iterative Linear-Quadratic Regulator. Solutions of optimized problems can be stored for warm-starting, and re-sampled at a different frequency while enforcing dynamic feasibility. The proposed framework is validated through a number of use-case scenarios involving several robotic platforms. Finally, an in-depth analysis of a specific case study is carried out, where a highly dynamic motion (i.e., a twisting jump using the quadruped robot Spot^® from BostonDynamics) is generated, in order to highlight the main features of the framework and demonstrate its capabilities.